diff --git a/trieste/acquisition/rule.py b/trieste/acquisition/rule.py
index 3c4376d727..dc172ab2a6 100644
--- a/trieste/acquisition/rule.py
+++ b/trieste/acquisition/rule.py
@@ -1010,8 +1010,8 @@ def update(
     def _get_tags(self, tags: Set[Tag]) -> Tuple[Set[Tag], Set[Tag]]:
         # Separate tags into local (matching index) and global tags (without matching
         # local tag).
-        local_gtags = set()
-        global_tags = set()
+        local_gtags = set()  # Set of global part of all local tags.
+        global_tags = set()  # Set of all global tags.
         for tag in tags:
             ltag = LocalizedTag.from_tag(tag)
             if not ltag.is_local:
diff --git a/trieste/objectives/utils.py b/trieste/objectives/utils.py
index d765feb13f..b074738ed1 100644
--- a/trieste/objectives/utils.py
+++ b/trieste/objectives/utils.py
@@ -22,13 +22,12 @@
 from collections.abc import Callable
 from typing import Mapping, Optional, Union, overload
 
-import tensorflow as tf
 from check_shapes import check_shapes
 
 from ..data import Dataset
 from ..observer import OBJECTIVE, MultiObserver, Observer, SingleObserver
 from ..types import Tag, TensorType
-from ..utils.misc import LocalizedTag
+from ..utils.misc import LocalizedTag, flatten_leading_dims
 
 
 @overload
@@ -83,7 +82,7 @@ def _observer(qps: TensorType) -> Mapping[Tag, Dataset]:
         # Call objective with rank 2 query points by flattening batch dimension.
         # Some objectives might only expect rank 2 query points, so this is safer.
         batch_size = qps.shape[1]
-        flat_qps = tf.reshape(qps, [-1, qps.shape[-1]])
+        flat_qps, unflatten = flatten_leading_dims(qps)
         obs_or_dataset = objective_or_observer(flat_qps)
 
         if not isinstance(obs_or_dataset, (Mapping, Dataset)):
@@ -98,8 +97,8 @@ def _observer(qps: TensorType) -> Mapping[Tag, Dataset]:
         for key, dataset in obs_or_dataset.items():
             # Include overall dataset and per batch dataset.
             flat_obs = dataset.observations
-            qps = tf.reshape(flat_qps, [-1, batch_size, flat_qps.shape[-1]])
-            obs = tf.reshape(flat_obs, [-1, batch_size, flat_obs.shape[-1]])
+            qps = unflatten(flat_qps)
+            obs = unflatten(flat_obs)
             datasets[key] = dataset
             for i in range(batch_size):
                 datasets[LocalizedTag(key, i)] = Dataset(qps[:, i], obs[:, i])